ANALYSIS OF THE ASYMPTOTIC CONVERGENCE OF PERIODIC SOLUTION OF THE MACKEY-GLASS EQUATION TO THE SOLUTION OF THE LIMIT RELAY EQUATION

The relaxation self-oscillations of the Mackey-Glass equation are studied under the assumption that the exponent in the nonlinearity denominator is a large parameter. We consider the case where the limit relay equation, which arises as the large parameter tends to infinity, has a periodic solution with the smallest number of breaking points on the period. In this case, we prove the existence of a periodic solution of the Mackey-Glass equation that is asymptotically close to the periodic solution of the limit equation.